NDLI: Edit lenses

Content Provider	ACM Digital Library
Author	Hofmann, Martin Pierce, Benjamin Wagner, Daniel
Abstract	A lens is a bidirectional transformation between a pair of connected data structures, capable of translating an edit on one structure into an appropriate edit on the other. Many varieties of lenses have been studied, but none, to date, has offered a satisfactory treatment of how edits are represented. Many foundational accounts only consider edits of the form "overwrite the whole structure," leading to poor behavior in many situations by failing to track the associations between corresponding parts of the structures when elements are inserted and deleted in ordered lists, for example. Other theories of lenses do maintain these associations, either by annotating the structures themselves with change information or using auxiliary data structures, but every extant theory assumes that the entire original source structure is part of the information passed to the lens. We offer a general theory of edit lenses, which work with descriptions of changes to structures, rather than with the structures themselves. We identify a simple notion of "editable structure"--a set of states plus a monoid of edits with a partial monoid action on the states--and construct a semantic space of lenses between such structures, with natural laws governing their behavior. We show how a range of constructions from earlier papers on "state-based" lenses can be carried out in this space, including composition, products, sums, list operations, etc. Further, we show how to construct edit lenses for arbitrary containers in the sense of Abbott, Altenkirch, and Ghani. Finally, we show that edit lenses refine a well-known formulation of state-based lenses, in the sense that every state-based lens gives rise to an edit lens over structures with a simple overwrite-only edit language, and conversely every edit lens on such structures gives rise to a state-based lens.
Starting Page	495
Ending Page	508
Page Count	14
File Format	PDF MP4
DOI	10.1145/2103621.2103715
Journal	ACM SIGPLAN Notices (SIGP)
Volume Number	47
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1983-05-01
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Algebra Bidirectional programming Edit Lens Symmetric
Content Type	Audio Text
Resource Type	Article

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